Estimation Procedure for Following Vapor Pressure Changes through Repeated Blending of Petroleum Stocks from Boiling Point Curves A practical method to estimate the vapor pressures of blended and reblended petroleum stocks that ensures air emissions stay within regulatory compliance limits.
In the business of managing heavy oil stocks, various safety and operational objectives, such as managing sulfur content or reducing viscosity, call for blending lighter products into the heavier oils. These cutters will commonly have higher volatilities than the base oil stock and this will impact the vapor pressure of the blend. following the vapor pressures that result from the various blend recipes. To ensure that air emissions for the tank stay within regulatory compliance limits, it would be beneficial if there were a practical method to estimate the vapor pressures of blended and reblended stocks before the blend is executed. Products are commonly stored in large tanks and accommodate repeated deliveries of smaller quantities; the frequent restocking of the tank with different additional products is not uncommon. Consequently, determining the applicable vapor pressure and the resulting emission losses from a tank on an ongoing basis would be a dynamic process. Heavier stocks do not normally need to be stored with extensive vapor emission controls such as floating roofs or emission treatment devices (e.g., absorption, condensation, incineration). These products are often heated to promote easier flow. Thus, knowledge of the blend vapor pressure at higher temperatures would allow a greater understanding of any additional allowable emissions. The blending of petroleum products to meet changing ultimate use specifications when the properties of both the source and constituent stocks are also changing calls for a flexible method of Speciation of all in-bound products of petroleum products particularly heavy oils is not easily accomplished and boiling point curves have historically been the most straight-forward vehicle to effectively accomplish product volatility characterization. These curves are developed following the ASTM D86 and ASTM 1160 protocols and a handful of laboratories in the United States have recently confirmed an ability to perform these protocols (along with ASTM 2887 and 7169 for heavier products) for less than $1,000 per sample. A procedure is presented here for the calculation of the anticipated vapor pressure for heavy oil cutter blends using such a boiling point characterization for each constituent component. The theoretical basis for this vapor pressure calculation of blends using historic petroleum refining engineering correlations is presented here along with a specific illustrative example for a 20-percent blend of the diesel into vacuum gas oil (VGO) for two temperatures (150 and 250 degrees Fahrenheit).!"#$"%&'(%")*+) *343,,** *34,,,** *2,,** *1,,** *0,,** */,,** *.,,** *-,,** *+,,** * * ) ),*.* 3,* 5,* +,* -,*.,* /,* 0,* 1,* 2,* 2.* 3,,* Volume,)-./(#") Percent Evaporated 6 Diesel VGO 6* * * * Volume Percent Evaporated 0 5 10 20 30 40 50 60 70 80 90 95 100 Diesel "Components" A B C D E F F 357 389 404 427 447 466 484 501 520 541 568 588 612 VGO "Components" G H I J K L F 506 637 659 706 745 772 802 835 867 908 961 1,004 1,011 Figure 1: Speciating with boiling point curves for diesel and virgin gas oil (VGO).
Estimation Procedure The elements (and assumptions) of this calculation are as follows: 1. The boiling point curves for the two constituents of the blend are characterized into quasi-component fractions (identified as fractions A L), as illustrated in Figure 1. 2. Since Raoult s Law treats the vapor pressure as a function of molar (rather than volumetric) concentrations, a molecular weight correlation with boiling point for what might normally be an intractable determination for these complex mixtures has been drawn from Nelson s Petroleum Refinery Engineering. 1 The API gravity of the respective blend stocks is a parameter used in this correlation. (API gravity is an inverse measure of a petroleum liquid's density relative to that of water, also known as specific gravity, and is used to compare densities of petroleum liquids.) Using the molecular weights, the volume fractions from the boiling point curves can then be converted to mole fractions (with the reasonable assumption of a uniform liquid density for all fractions). 3. Vapor pressures have been well-characterized as a function of boiling points 1 and the nomograph in Meyer 2 is a generally accepted source for determining them for each of the separate fractions. When these are determined at various temperatures (e.g., 150 and 250 degrees Fahrenheit, as illustrated here), they can then be used to develop simplified Antoine equation correlations Diesel D Range A B C D E F 1 B.P. in of 390 425 470 500 540 580 API 38 38 38 38 38 38 M.W. 150 170 185 203 236 248 5 VP @ 150 0.115 0.042 0.012 0.0055 0.0015 0.003 VP @ 250 1.4 0.7 0.28 0.15 0.07 0.02 8 Vol% in D 10 20 20 20 20 10 Moles 0.066666667 0.117647059 0.108108108 0.098522167 0.084745763 0.040322581 Mol% 0.1292 0.2280 0.2095 0.1909 0.1642 0.0781 12 Vol% in V Moles Mol% 16 Antoine: ln p* = A + B/(oF + 460) B 2082.746 2344.509 2624.902 2754.906 3202.525 1580.933 A 3.270 2.945 2.424 1.983 1.851-1.685 BLENDS: 21 Mix of 20% D with 80%V at 250oF: pi = pi*xi D 0.180878553 0.159598723 0.058663314 0.028640165 0.011496518 0.001562891 V Aggregate vp 0.089138387 psi (.44084 x 0.2 + 0.001213 x 0.8) 26 Mix of 20%D with 80%V at 150oF D 0.014857881 0.009575923 0.002514142 0.001050139 0.000246354 0.000234434 V Aggregate vp 0.005854247 psi (.028479 x 0.2 + 0.000198 x 0.8) Figure 2: Vapor pressure blend calculation at various temperatures for VGO cut with diesel. Notes: Line 1: Boiling points for component segments for diesel (columns A F) and VGO (columns G L) in Figure 1. Line 2: API gravity from laboratory. Line 3: Molecular weights. 1 Lines 5 and 6: Vapor pressures for segments tested at 150 and 250 degrees Fahrenheit. 2
for the vapor pressure contributions of the respective fractions at other temperatures (i.e., using the parameters A and B in Antoine s equation: ln p* = A + B/T). 4. Raoult s Law can then be used to determine the aggregate vapor pressure of the blend for the 20-percent blend of diesel into VGO at 150 and 250 degrees Fahrenheit, respectively, as shown in Figure 2. This procedure can be followed before the blend is actually performed and the resulting aggregate boiling point curve for that blend can be used as a constituent in further blending with other stocks. A calibration of this use of the boiling point curves to provide the basis of determining the vapor pressure can be accomplished by comparison with the results from the more protracted laboratory vapor pressure determinations (currently outlined in the ASTM D2879 protocol). Representative Scenario Figure 2 illustrates this representative scenario: Consider two tanks involved in the blending process. Tank A1 contains some 60,000 barrels of the heavier VGO. Tank B contains 30,000 barrels of the lighter diesel cutter stock. When 12,000 barrels of cutter are blended into A1, the resulting blend of 72,000 barrels (now called A2) is the 20-percent blend for which the vapor pressure is calculated in the spreadsheet. The projected vapor VGO V G H I J K L 635 705 775 830 910 990 23 23 23 23 23 23 260 310 360 430 525 620 0.001 0.0002 0 0 0 0 0.0065 0.001 0 0 0 0 sum 0.516012344 10 20 20 20 20 10 sum 0.038461538 0.064516129 0.055555556 0.046511628 0.038095238 0.016129032 0.259269121 0.1483 0.2488 0.2143 0.1794 0.1469 0.0622 0.440840165 0.000964134 0.000248809 0 0 0 0 0.001212943 0.028478874 0.000148328 4.97618E-05 0 0 0 0 0.00019809 Figure 2: Vapor pressure blend calculation at various temperatures for VGO cut with diesel. (continued) Lines 8 and 12: Volume percentages associated with segments for diesel and VGO, respectively. Lines 9 and 13: Moles for each segment (using uniform liquid densities). Lines 10 and 14: Mole fraction of each segment. Lines 16 to 18: Reduction of vapor pressures from Lines 5 and 6 to Antoine s equation. Lines 21 to 24: Use of Raoult s Law to determine blend vapor pressure at 250 degrees Fahrenheit. Lines 26 to 29: Use of Raoult s Law to determine blend vapor pressure at 150 degrees Fahrenheit.
pressure in A2 would thus be some 0.0058 psi at 150 degrees Fahrenheit (the presumed temperature of A and A1 at the outset). Were this blended A2 be heated to 250 degrees Fahrenheit, the resulting vapor pressure is projected to become 0.2 x 0.441 + 0.8 x 0.0012 or 0.0891 psi. 1. Determining the temperature of liquid and vapor spaces in the tank. 2. A reasonable assessment of the air volume displaced when product is added to a tank. Clearly, the volatility of the cutter stock determines the blend vapor pressure. This vapor pressure (0.0058 psi) can then be the basis for determining the petroleum contaminant (VOC) level in the displaced air resulting from the addition of 12,000 barrels when blending occurs in A1. The vapor pressure of the pre-blended VGO (0.0002 psi) is thus meaningfully increased through the addition of the cutter. This post-blend vapor pressure is also relevant to the emissions when the tank is breathing in tank A2. Should additional stock then be added to A2 (e.g., from a putative Tank C or from newly imported product), the above calculation can be repeated with this stock being added to the last characterization of Tank A2. Summary The tasks facing the engineer responsible for accounting for emissions from movements in heavy oil storage tanks are these: 3. Determining the changing vapor pressures after the blends are conducted. This vapor pressure can either come from (a) tracking product concentrations through the discussed boiling point characterization obtained at the entry of each product into the blender s custody; (b) the generally formidable analytical speciation for these heavier petroleum blends; or (c) the continuing ex-post-facto sampling and laboratory vapor pressure determination. 4. A corollary comment is that when regulatory requirements include determination of the emission of particular hazardous air pollutants, these can be entered into the calculation as a parallel constituent to the pseudo-components derived from segmenting the boiling point curves for the petroleum constituents. em Robert E.C. Weaver, Ph.D., P.E. (retired), formerly Principal, International Technical Management, International-Matex Tank Terminals, and Dean of Engineering, University of Tennessee. E-mail: Bobweaver@imtt.com; bobweaverpe@yahoo.com. Bibliography 1. Nelson, W.L. Petroleum Refinery Engineering: McGraw Hill, 1949; p. 146 and p. 173. 2. Meyer. Vapor Pressure Curves of Petroleum Spirits; J. Inst. Pet. Tech. 1931, 17, 42. 3. Hougen and Watson. Chemical Process Principles: Wiley & Sons, 1947. 4. ASTM D86, Standard Test Method for Distillation of Petroleum Products. 5. ASTM D1160, Standard Test Method for Distillation of Petroleum Products at Reduced Pressures. 6. ASTM D2879, Standard Test Method of Vapor Pressure-Temperature Relationship.